I am stuck with a problem in general topology. First of all, recall that a space $X$ is KC if every compact subset of $X$ is closed, and is weak Hausdorff if for all $u:K\rightarrow X$ continuous (where $K$ is compact Hausdorff) $u(K)$ is closed in $X$.
It's clear that KC implies weak Hausdorff. I tried to find a space that is weak Hausdorff and not KC but it looks tough (I don't even know if that's possible), does anyone have an idea ?
Thanks in advance.